R Notebook

library(dplyr)

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

    filter, lag

The following objects are masked from ‘package:base’:

    intersect, setdiff, setequal, union

library(tidyverse)

Warning: package ‘tidyverse’ was built under R version 4.2.3Warning: package ‘ggplot2’ was built under R version 4.2.3Warning: package ‘tidyr’ was built under R version 4.2.3Warning: package ‘readr’ was built under R version 4.2.3Warning: package ‘purrr’ was built under R version 4.2.3Warning: package ‘forcats’ was built under R version 4.2.3Warning: package ‘lubridate’ was built under R version 4.2.3── Attaching core tidyverse packages ─────────────────────────────────── tidyverse 2.0.0 ──
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library(tidyr)
library(plotly)

Warning: package ‘plotly’ was built under R version 4.2.3Registered S3 method overwritten by 'data.table':
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Attaching package: ‘plotly’

The following object is masked from ‘package:ggplot2’:

    last_plot

The following object is masked from ‘package:stats’:

    filter

The following object is masked from ‘package:graphics’:

    layout

library(ggplot2)
library(coefplot)

Warning: package ‘coefplot’ was built under R version 4.2.3

library(corrplot)

Warning: package ‘corrplot’ was built under R version 4.2.3corrplot 0.92 loaded

library(plotly)
library(caTools)

Warning: package ‘caTools’ was built under R version 4.2.3

library(Metrics)

Warning: package ‘Metrics’ was built under R version 4.2.3

mathData = read.csv('studentMat.csv')
porData = read.csv('studentPor.csv')

#EDA

school - student’s school (binary: ‘GP’ - Gabriel Pereira or ‘MS’ - Mousinho da Silveira) 2. sex - student’s sex (binary: ‘F’ - female or ‘M’ - male) 3. age - student’s age (numeric: from 15 to 22) 4. address - student’s home address type (binary: ‘U’ - urban or ‘R’ - rural) 5. famsize - family size (binary: ‘LE3’ - less or equal to 3 or ‘GT3’ - greater than 3) 6. Pstatus - parent’s cohabitation status (binary: ‘T’ - living together or ‘A’ - apart) 7. Medu - mother’s education (numeric: 0 - none, 1 - primary education (4th grade), 2 – 5th to 9th grade, 3 – secondary education or 4 – higher education) 8. Fedu - father’s education (numeric: 0 - none, 1 - primary education (4th grade), 2 – 5th to 9th grade, 3 – secondary education or 4 – higher education) 9. Mjob - mother’s job (nominal: ‘teacher’, ‘health’ care related, civil ‘services’ (e.g. administrative or police), ‘at_home’ or ‘other’) 10. Fjob - father’s job (nominal: ‘teacher’, ‘health’ care related, civil ‘services’ (e.g. administrative or police), ‘at_home’ or ‘other’) 11. reason - reason to choose this school (nominal: close to ‘home’, school ‘reputation’, ‘course’ preference or ‘other’) 12. guardian - student’s guardian (nominal: ‘mother’, ‘father’ or ‘other’) 13. traveltime - home to school travel time (numeric: 1 - 1 hour) 14. studytime - weekly study time (numeric: 1 - 10 hours) 15. failures - number of past class failures (numeric: n if 1<=n<3, else 4) 16. schoolsup - extra educational support (binary: yes or no) 17. famsup - family educational support (binary: yes or no) 18. paid - extra paid classes within the course subject (Math or Portuguese) (binary: yes or no) 19. activities - extra-curricular activities (binary: yes or no) 20. nursery - attended nursery school (binary: yes or no) higher - wants to take higher education (binary: yes or no) 22. internet - Internet access at home (binary: yes or no) 23. romantic - with a romantic relationship (binary: yes or no) 24. famrel - quality of family relationships (numeric: from 1 - very bad to 5 - excellent) 25. freetime - free time after school (numeric: from 1 - very low to 5 - very high) 26. goout - going out with friends (numeric: from 1 - very low to 5 - very high) 27. Dalc - workday alcohol consumption (numeric: from 1 - very low to 5 - very high) 28. Walc - weekend alcohol consumption (numeric: from 1 - very low to 5 - very high) 29. health - current health status (numeric: from 1 - very bad to 5 - very good) 30. absences - number of school absences (numeric: from 0 to 93

mathData

porData

NA

Creating Plots for our datasets

ggplot(porData, aes(x = school)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Which school are they",
    x = "School",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

Gabriel Pereira

Mousinho da Silveira

ggplot(mathData, aes(x = school)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Which school are they",
    x = "School",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(porData, aes(x = sex)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Count of Males and Females ",
    x = "Sex",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(mathData, aes(x = sex)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Count of Males and Females ",
    x = "Sex",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(porData, aes(x = as.factor(age))) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Count of Students by Age",
    x = "Age",
    y = "Count"
  ) + stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +
  theme_minimal()

ggplot(mathData, aes(x = as.factor(age))) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Count of Students by Age",
    x = "Age",
    y = "Count"
  ) + stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +
  theme_minimal()

boxplot(porData$age, horizontal=TRUE, main="Horizontal Box Plot of Data", xlab="Value", col="#FF6666")

boxplot(mathData$age, horizontal=TRUE, main="Horizontal Box Plot of Data", xlab="Value", col="skyblue")

ggplot(porData, aes(x = address)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " By where does student live",
    x = "Area",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(mathData, aes(x = address)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " By where does student live",
    x = "Area",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(porData, aes(x = famsize)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " By family size ",
    x = "No of people",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

Greater than 3

Less than 3

ggplot(mathData, aes(x = famsize)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " By family size ",
    x = "No of people",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(porData, aes(x = Pstatus)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Parents living status ",
    x = "Status",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

Apart

Together

ggplot(mathData, aes(x = Pstatus)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Parents living status ",
    x = "Status",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(porData, aes(x = factor(Medu))) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Mother's Education",
    x = "Education",
    y = "Count"
  ) +
  theme_minimal() +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

mother’s education (numeric: 0 - none, 1 - primary education (4th grade), 2 – 5th to 9th grade, 3 – secondary education or 4 – higher education)

ggplot(mathData, aes(x = factor(Medu))) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Mother's Education",
    x = "Education",
    y = "Count"
  ) +
  theme_minimal() +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(porData, aes(x = factor(Fedu))) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Father's Education",
    x = "Education",
    y = "Count"
  ) +
  theme_minimal() +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

father’s education (numeric: 0 - none, 1 - primary education (4th grade), 2 – 5th to 9th grade, 3 – secondary education or 4 – higher education)

ggplot(mathData, aes(x = factor(Fedu))) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Father's Education",
    x = "Education",
    y = "Count"
  ) +
  theme_minimal() +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(porData, aes(x = Mjob)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Mother's Job",
    x = "Job",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(mathData, aes(x = Mjob)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Mother's Job",
    x = "Job",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(porData, aes(x = Fjob)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Father's Job",
    x = "Job",
    y = "Count"
  ) +
  theme_minimal() +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(mathData, aes(x = Fjob)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Father's Job",
    x = "Job",
    y = "Count"
  ) +
  theme_minimal() +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(porData, aes(x = reason)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Reason to select the school",
    x = "Reason",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(mathData, aes(x = reason)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Reason to select the school",
    x = "Reason",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(porData, aes(x = guardian)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Guardians",
    x = "Gaurdian",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(mathData, aes(x = guardian)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Guardians",
    x = "Gaurdian",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(porData, aes(x = traveltime)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Traveltime for schools by hour",
    x = "Traveltime",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(mathData, aes(x = traveltime)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Traveltime for schools by hour",
    x = "Traveltime",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(porData, aes(x = studytime)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Study preparation by hours",
    x = "studytime",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(mathData, aes(x = studytime)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Study preparation by hours",
    x = "studytime",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(porData, aes(x = failures)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Failures in past",
    x = "Failure",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(mathData, aes(x = failures)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Failures in past",
    x = "Failure",
    y = "Count"
  ) +
  theme_minimal()+
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5)

ggplot(porData, aes(x = schoolsup)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " School support ",
    x = "support",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(mathData, aes(x = schoolsup)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " School support ",
    x = "support",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(porData, aes(x = famsup)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " family support ",
    x = "support",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(mathData, aes(x = famsup)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " family support ",
    x = "support",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(porData, aes(x = paid)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Are they gng for extra paid classes ",
    x = "Paid classes",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(mathData, aes(x = paid)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Are they gng for extra paid classes ",
    x = "Paid classes",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(porData, aes(x = activities)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Extracurricular activities",
    x = "Extra",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +
  theme_minimal()

ggplot(mathData, aes(x = activities)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Extracurricular activities",
    x = "Extra",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +
  theme_minimal()

ggplot(porData, aes(x = nursery)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Attended nursery school or not ",
    x = "Nursery",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(mathData, aes(x = nursery)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Attended nursery school or not ",
    x = "Nursery",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(porData, aes(x = higher)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Are they planning on taking higher studies",
    x = "Higher studies",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(mathData, aes(x = higher)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Are they planning on taking higher studies",
    x = "Higher studies",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(porData, aes(x = internet)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = "Internet acess at home",
    x = "Internet",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(mathData, aes(x = internet)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = "Internet acess at home",
    x = "Internet",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(porData, aes(x = romantic)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Are they in romantic relationship ",
    x = "Relationship",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(mathData, aes(x = romantic)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Are they in romantic relationship ",
    x = "Relationship",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(porData, aes(x = famrel)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Family Relationship ",
    x = "Famrel",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(mathData, aes(x = famrel)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Family Relationship ",
    x = "Famrel",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

Bad to Excellent

ggplot(porData, aes(x = freetime)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " How much freetime ",
    x = "Free time",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(mathData, aes(x = freetime)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " How much freetime ",
    x = "Free time",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

Low to high

ggplot(porData, aes(x = goout)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Are they gng out with frnds ",
    x = "gng out with frnds",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(mathData, aes(x = goout)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Are they gng out with frnds ",
    x = "gng out with frnds",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

Low to high

ggplot(porData, aes(x = Dalc)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Workday alc consump ",
    x = "Drinking alc",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(mathData, aes(x = Dalc)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Workday alc consump ",
    x = "Drinking alc",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

Low to high

ggplot(porData, aes(x = Walc)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Weekend alc consump ",
    x = "Drinking alc",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(mathData, aes(x = Walc)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Weekend alc consump ",
    x = "Drinking alc",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

Low to high

ggplot(porData, aes(x = health)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Health Status ",
    x = "Health",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

ggplot(mathData, aes(x = health)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Health Status ",
    x = "Health",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) + 
  theme_minimal()

Bad to Good

ggplot(porData, aes(x = absences)) +
  geom_bar(fill = "#FF6666") +
  labs(
    title = " Absent days ",
    x = "No of days",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

ggplot(mathData, aes(x = absences)) +
  geom_bar(fill = "skyblue") +
  labs(
    title = " Absent days ",
    x = "No of days",
    y = "Count"
  ) +
  stat_count(geom = "text", aes(label = ..count..), vjust = -0.5) +  
  theme_minimal()

Data Preprocessing

Separating Numeric and Non numeric Data

non_numeric_columns <- names(porData)[sapply(porData, function(col) !is.numeric(col))]
cat("These are non-numeric columns:", non_numeric_columns, "\n\n")

These are non-numeric columns: school sex address famsize Pstatus Mjob Fjob reason guardian schoolsup famsup paid activities nursery higher internet romantic 

numeric_columns <- names(porData)[sapply(porData, is.numeric)]
cat("These are numeric columns:", numeric_columns, "\n")

These are numeric columns: age Medu Fedu traveltime studytime failures famrel freetime goout Dalc Walc health absences G1 G2 G3 

Checking all the unique values that a non Numeric feature has

non_numeric <- names(porData)[sapply(porData, function(col) !is.numeric(col))]

for (col in non_numeric){
  print(paste("The column ", col, "has ", length(unique(porData[[col]])), ' unique values they are: '))
  print((unique(porData[[col]])))
  cat('\n')
}

[1] "The column  school has  2  unique values they are: "
[1] "GP" "MS"

[1] "The column  sex has  2  unique values they are: "
[1] "F" "M"

[1] "The column  address has  2  unique values they are: "
[1] "U" "R"

[1] "The column  famsize has  2  unique values they are: "
[1] "GT3" "LE3"

[1] "The column  Pstatus has  2  unique values they are: "
[1] "A" "T"

[1] "The column  Mjob has  5  unique values they are: "
[1] "at_home"  "health"   "other"    "services" "teacher" 

[1] "The column  Fjob has  5  unique values they are: "
[1] "teacher"  "other"    "services" "health"   "at_home" 

[1] "The column  reason has  4  unique values they are: "
[1] "course"     "other"      "home"       "reputation"

[1] "The column  guardian has  3  unique values they are: "
[1] "mother" "father" "other" 

[1] "The column  schoolsup has  2  unique values they are: "
[1] "yes" "no" 

[1] "The column  famsup has  2  unique values they are: "
[1] "no"  "yes"

[1] "The column  paid has  2  unique values they are: "
[1] "no"  "yes"

[1] "The column  activities has  2  unique values they are: "
[1] "no"  "yes"

[1] "The column  nursery has  2  unique values they are: "
[1] "yes" "no" 

[1] "The column  higher has  2  unique values they are: "
[1] "yes" "no" 

[1] "The column  internet has  2  unique values they are: "
[1] "no"  "yes"

[1] "The column  romantic has  2  unique values they are: "
[1] "no"  "yes"

Separating Binary & Multiple unique values within features

binary_columns <- c()
multi_unique_columns <- c()


for (col in non_numeric) {
    num_unique <- length(unique(porData[[col]]))
    
    if (num_unique == 2) {
        binary_columns <- c(binary_columns, col)
    } else if (num_unique > 2) {
        multi_unique_columns <- c(multi_unique_columns, col)
    }
}


print(paste("Binary columns:", paste(binary_columns, collapse = ", ")))

[1] "Binary columns: school, sex, address, famsize, Pstatus, schoolsup, famsup, paid, activities, nursery, higher, internet, romantic"

cat('\n')

print(paste("Multi unique value columns:", paste(multi_unique_columns, collapse = ", ")))

[1] "Multi unique value columns: Mjob, Fjob, reason, guardian"

Turing binary unique values into numeric

If a features has value ‘yes’ it’s encoded as 1, ‘no’ as 0. Rest all shown below.

cat('----Portugese Data----\n\n')

----Portugese Data----

for (col in binary_columns) {
  if ("yes" %in% porData[[col]] && "no" %in% porData[[col]]) {
   
    porData[[col]] <- ifelse(porData[[col]] == "yes", 1, 0)
    
  } else {
    
    unique_vals <- unique(porData[[col]])
    porData[[col]] <- ifelse(porData[[col]] == unique_vals[1], 0, 1)
    print(paste("Portugese's Feature:",col, ' is encoded ', unique_vals[1],' as 0 ', unique_vals[2],' as 1'))
  }
}

[1] "Portugese's Feature: school  is encoded  GP  as 0  MS  as 1"
[1] "Portugese's Feature: sex  is encoded  F  as 0  M  as 1"
[1] "Portugese's Feature: address  is encoded  U  as 0  R  as 1"
[1] "Portugese's Feature: famsize  is encoded  GT3  as 0  LE3  as 1"
[1] "Portugese's Feature: Pstatus  is encoded  A  as 0  T  as 1"

cat('\n----Math Data----\n\n')

----Math Data----

# Doing for Math data too
for (col in binary_columns) {
  if ("yes" %in% mathData[[col]] && "no" %in% mathData[[col]]) {
   
    mathData[[col]] <- ifelse(mathData[[col]] == "yes", 1, 0)
    
  } else {
    
    unique_vals <- unique(mathData[[col]])
    mathData[[col]] <- ifelse(mathData[[col]] == unique_vals[1], 0, 1)
    print(paste("Math's Feature:",col, ' is encoded ', unique_vals[1],' as 0 ', unique_vals[2],' as 1'))
  }
}

[1] "Math's Feature: school  is encoded  GP  as 0  MS  as 1"
[1] "Math's Feature: sex  is encoded  F  as 0  M  as 1"
[1] "Math's Feature: address  is encoded  U  as 0  R  as 1"
[1] "Math's Feature: famsize  is encoded  GT3  as 0  LE3  as 1"
[1] "Math's Feature: Pstatus  is encoded  A  as 0  T  as 1"

Performing 1-hot encoding for Multivalued columns

cat('----Portugese Data----\n\n')

----Portugese Data----

for (col in multi_unique_columns) {
  
  formula_str <- paste("~ 0 +", col)
  one_hot <- model.matrix(as.formula(formula_str), data = porData)
  
  
  one_hot_df <- as.data.frame(one_hot)
  colnames(one_hot_df) <- gsub("^.\\.", col, colnames(one_hot_df))
  
  
  porData <- cbind(porData, one_hot_df)
  
  
  porData[[col]] <- NULL
}
head(porData)

cat('\n----Math Data----\n\n')

----Math Data----

# for Math data
for (col in multi_unique_columns) {

  formula_str <- paste("~ 0 +", col)
  one_hot <- model.matrix(as.formula(formula_str), data = mathData)


  one_hot_df <- as.data.frame(one_hot)
  colnames(one_hot_df) <- gsub("^.\\.", col, colnames(one_hot_df))


  mathData <- cbind(mathData, one_hot_df)


  mathData[[col]] <- NULL
}
head(mathData)

What determines student success in school measured by their test scores

We’ll Focus only on Grade 3(G3) which is the final Grade

Mothers education or Fathers education

Fathers Education

#Por's Model
modelPor_Fedu <- lm(G3 ~ Fedu, data = porData)
summary(modelPor_Fedu)

Call:
lm(formula = G3 ~ Fedu, data = porData)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.9594  -1.7153  -0.0932   2.0406   7.9068 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  10.4711     0.2883  36.314  < 2e-16 ***
Fedu          0.6221     0.1129   5.512 5.12e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.16 on 647 degrees of freedom
Multiple R-squared:  0.04486,   Adjusted R-squared:  0.04338 
F-statistic: 30.39 on 1 and 647 DF,  p-value: 5.117e-08

plot(porData$Fedu, porData$G3, main="Fathers's Education (Fedu) vs. Final Grade (G3) for Portuguese Data", xlab="Father's Education", ylab="Final Grade (G3)")
abline(modelPor_Fedu, col="red")

#Math's Model
modelMath_Fedu <- lm(G3 ~ Fedu, data = mathData)
summary(modelMath_Fedu)

Call:
lm(formula = G3 ~ Fedu, data = mathData)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.3642  -1.9014   0.5614   2.9196   9.2777 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   8.7967     0.5763  15.264  < 2e-16 ***
Fedu          0.6419     0.2099   3.058  0.00238 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.534 on 393 degrees of freedom
Multiple R-squared:  0.02324,   Adjusted R-squared:  0.02076 
F-statistic: 9.352 on 1 and 393 DF,  p-value: 0.00238

plot(mathData$Fedu, mathData$G3, main="Fathers's Education (Fedu) vs. Final Grade (G3) for Math Data", xlab="Father's Education", ylab="Final Grade (G3)")
abline(modelMath_Fedu, col="red")

Mothers Education

modelPor_Medu <- lm(G3 ~ Medu, data = porData)
summary(modelPor_Medu)

Call:
lm(formula = G3 ~ Medu, data = porData)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.9217  -1.5541   0.0783   2.0783   7.1298 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  10.1864     0.2998  33.982  < 2e-16 ***
Medu          0.6838     0.1087   6.293 5.75e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.139 on 647 degrees of freedom
Multiple R-squared:  0.05767,   Adjusted R-squared:  0.05622 
F-statistic:  39.6 on 1 and 647 DF,  p-value: 5.752e-10

plot(porData$Medu, porData$G3, main="Mother's Education (Medu) vs. Final Grade (G3) for Portuguese Data", xlab="Mother's Education", ylab="Final Grade (G3)")
abline(modelPor_Medu, col="red")

#Math's Model
modelMath_Medu <- lm(G3 ~ Medu, data = mathData)
summary(modelMath_Medu)

Call:
lm(formula = G3 ~ Medu, data = mathData)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.5517  -1.7342   0.4483   3.2202   9.2658 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   7.9167     0.6097   12.98  < 2e-16 ***
Medu          0.9088     0.2061    4.41 1.34e-05 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.478 on 393 degrees of freedom
Multiple R-squared:  0.04715,   Adjusted R-squared:  0.04473 
F-statistic: 19.45 on 1 and 393 DF,  p-value: 1.336e-05

plot(mathData$Medu, mathData$G3, main="Mother's Education (Medu) vs. Final Grade (G3) for Math Data ", xlab="Mother's Education", ylab="Final Grade (G3)")
abline(modelMath_Medu, col="red")

Let’s look Combination of Both Mother’s and Father’s Education impact on your test scores

modelPor_Edu <- lm(G3 ~ Medu + Fedu , data = porData)
summary(modelPor_Edu)

Call:
lm(formula = G3 ~ Medu + Fedu, data = porData)

Residuals:
     Min       1Q   Median       3Q      Max 
-13.1385  -1.5689  -0.0537   1.9463   7.5159 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   9.9791     0.3176   31.42  < 2e-16 ***
Medu          0.5051     0.1423    3.55 0.000414 ***
Fedu          0.2848     0.1468    1.94 0.052793 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.132 on 646 degrees of freedom
Multiple R-squared:  0.06313,   Adjusted R-squared:  0.06023 
F-statistic: 21.77 on 2 and 646 DF,  p-value: 7.115e-10

coefplot(modelPor_Edu)

modelMath_Edu <- lm(G3 ~ Medu + Fedu , data = mathData)
summary(modelMath_Edu)

Call:
lm(formula = G3 ~ Medu + Fedu, data = mathData)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.6344  -1.7275   0.3901   3.2260   9.2725 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   7.8205     0.6478  12.073  < 2e-16 ***
Medu          0.8359     0.2638   3.168  0.00165 ** 
Fedu          0.1176     0.2654   0.443  0.65796    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.482 on 392 degrees of freedom
Multiple R-squared:  0.04763,   Adjusted R-squared:  0.04277 
F-statistic: 9.802 on 2 and 392 DF,  p-value: 7.013e-05

coefplot(modelMath_Edu)

Does spending more time on studying actually improves grades

modelPor_Study = lm(G3 ~ studytime, data=porData)
summary(modelPor_Study)

Call:
lm(formula = G3 ~ studytime, data = porData)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.9735  -1.9463   0.0265   2.0265   7.0265 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  10.0278     0.3115  32.191  < 2e-16 ***
studytime     0.9728     0.1483   6.562 1.09e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.131 on 647 degrees of freedom
Multiple R-squared:  0.06239,   Adjusted R-squared:  0.06095 
F-statistic: 43.06 on 1 and 647 DF,  p-value: 1.091e-10

plot(porData$studytime, porData$G3, main="Study Time (studytime) vs. Final Grade (G3) for Portuguese Data", xlab="Study time", ylab="Final Grade (G3)")
abline(modelPor_Study, col="red")

modelMath_Study <- lm(G3 ~ studytime, data=mathData)
summary(modelMath_Study)

Call:
lm(formula = G3 ~ studytime, data = mathData)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.4643  -1.8623   0.5357   3.0697   9.1377 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   9.3283     0.6033  15.463   <2e-16 ***
studytime     0.5340     0.2741   1.949   0.0521 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.565 on 393 degrees of freedom
Multiple R-squared:  0.009569,  Adjusted R-squared:  0.007049 
F-statistic: 3.797 on 1 and 393 DF,  p-value: 0.05206

plot(mathData$studytime, mathData$G3, main="Study Time (studytime) vs. Final Grade (G3) for Math Data", xlab="Study time", ylab="Final Grade (G3)")
abline(modelMath_Study, col="red")

NA
NA
NA

Problem with above data is data is ordinal and range is limited How to deal with ordinal data in Regression: https://stats.stackexchange.com/questions/164689/ordinal-data-in-regression

absences - number of school absences (numeric: from 0 to 93)

modelPor_Absences <- lm(G3 ~ absences, data=porData)
summary(modelPor_Absences)

Call:
lm(formula = G3 ~ absences, data = porData)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.1388  -1.8207  -0.1388   1.9884   7.1157 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 12.13880    0.16099  75.399   <2e-16 ***
absences    -0.06361    0.02725  -2.334   0.0199 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.22 on 647 degrees of freedom
Multiple R-squared:  0.00835,   Adjusted R-squared:  0.006817 
F-statistic: 5.448 on 1 and 647 DF,  p-value: 0.0199

plot(porData$absences, porData$G3, main="Absences vs. Final Grade (G3) for Portuguese Data", xlab="Number of Absences", ylab="Final Grade (G3)")
abline(modelPor_Absences, col="red")

modelMath_Absences <- lm(G3 ~ absences, data=mathData)
summary(modelMath_Absences)

Call:
lm(formula = G3 ~ absences, data = mathData)

Residuals:
     Min       1Q   Median       3Q      Max 
-10.3033  -2.3033   0.5007   3.4811   9.6183 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 10.30327    0.28347  36.347   <2e-16 ***
absences     0.01961    0.02886   0.679    0.497    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.585 on 393 degrees of freedom
Multiple R-squared:  0.001173,  Adjusted R-squared:  -0.001369 
F-statistic: 0.4615 on 1 and 393 DF,  p-value: 0.4973

plot(mathData$absences, mathData$G3, main="Absences vs. Final Grade (G3) for Math Data", xlab="Number of Absences", ylab="Final Grade (G3)")
abline(modelMath_Absences, col="red")

multiplot(modelPor_Absences, modelMath_Absences, names=c("Portuguese Model", "Math Model"))

NA
NA

Alcohol Consumption

Daily Alcohol Consumption

modelPor_Dalc <- lm(G3 ~ Dalc, data=porData)
summary(modelPor_Dalc)

Call:
lm(formula = G3 ~ Dalc, data = porData)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.2652  -1.5501  -0.2652   1.7348   7.1650 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  12.9804     0.2371   54.75  < 2e-16 ***
Dalc         -0.7151     0.1344   -5.32 1.43e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.165 on 647 degrees of freedom
Multiple R-squared:  0.04191,   Adjusted R-squared:  0.04043 
F-statistic:  28.3 on 1 and 647 DF,  p-value: 1.432e-07

plot(porData$Dalc, porData$G3, main="Workday Alcohol Consumption (Dalc) vs. Final Grade (G3) for Portuguese Data", xlab="Dalc", ylab="Final Grade (G3)")
abline(modelPor_Dalc, col="red")

modelMath_Dalc <- lm(G3 ~ Dalc, data=mathData)
summary(modelMath_Dalc)

Call:
lm(formula = G3 ~ Dalc, data = mathData)

Residuals:
     Min       1Q   Median       3Q      Max 
-10.5504  -1.9881   0.4496   3.4496   9.4496 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  10.8316     0.4476  24.201   <2e-16 ***
Dalc         -0.2811     0.2591  -1.085    0.278    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.58 on 393 degrees of freedom
Multiple R-squared:  0.002988,  Adjusted R-squared:  0.0004508 
F-statistic: 1.178 on 1 and 393 DF,  p-value: 0.2785

plot(mathData$Dalc, mathData$G3, main="Workday Alcohol Consumption (Dalc) vs. Final Grade (G3) for Math Data", xlab="Dalc", ylab="Final Grade (G3)")
abline(modelMath_Dalc, col="red")

multiplot(modelPor_Dalc,modelMath_Dalc, names=c('Daily Alc consumption for Portuguese Data', 'Daily Alc consumption for Math Data'))

Weekly Alcohol consumption

modelPor_Walc <- lm(G3 ~ Walc, data=porData)
summary(modelPor_Walc)

Call:
lm(formula = G3 ~ Walc, data = porData)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.4748  -1.5863  -0.0306   1.9694   7.8579 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 12.91911    0.25470  50.723   <2e-16 ***
Walc        -0.44426    0.09733  -4.564    6e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.182 on 647 degrees of freedom
Multiple R-squared:  0.03119,   Adjusted R-squared:  0.0297 
F-statistic: 20.83 on 1 and 647 DF,  p-value: 5.999e-06

plot(porData$Walc, porData$G3, main="Weekend Alcohol Consumption (Walc) vs. Final Grade (G3) for Portuguese Data", xlab="Walc", ylab="Final Grade (G3)")
abline(modelPor_Walc, col="red")

modelMath_Walc <- lm(G3 ~ Walc, data=mathData)
summary(modelMath_Walc)

Call:
lm(formula = G3 ~ Walc, data = mathData)

Residuals:
     Min       1Q   Median       3Q      Max 
-10.6537  -2.0071   0.3463   3.3463   9.3463 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  10.8385     0.4708  23.019   <2e-16 ***
Walc         -0.1848     0.1792  -1.031    0.303    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.581 on 393 degrees of freedom
Multiple R-squared:  0.002698,  Adjusted R-squared:  0.00016 
F-statistic: 1.063 on 1 and 393 DF,  p-value: 0.3032

plot(mathData$Walc, mathData$G3, main="Weekend Alcohol Consumption (Walc) vs. Final Grade (G3) for Math Data", xlab="Walc", ylab="Final Grade (G3)")
abline(modelMath_Walc, col="red")

multiplot(modelPor_Walc,modelMath_Walc, names=c('Weekly Alc consumption for Portuguese Data', 'Weekly Alc consumption for Math Data'))

Overview of all coeff’s till now

multiplot(modelPor_Dalc,modelMath_Dalc,modelPor_Walc,modelMath_Walc, names=c('Daily Alc consumption for Portuguese Data', 'Daily Alc consumption for Math Data','Weekly Alc consumption for Portuguese Data', 'Weekly Alc consumption for Math Data'))

modelPor_Multi <- lm(G3 ~ Medu + Fedu + studytime + Dalc + Walc , data = porData)
summary(modelPor_Multi)

Call:
lm(formula = G3 ~ Medu + Fedu + studytime + Dalc + Walc, data = porData)

Residuals:
    Min      1Q  Median      3Q     Max 
-12.899  -1.522   0.149   1.790   7.997 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   9.6366     0.4839  19.913  < 2e-16 ***
Medu          0.4275     0.1368   3.125  0.00186 ** 
Fedu          0.3117     0.1409   2.213  0.02724 *  
studytime     0.7796     0.1459   5.342 1.28e-07 ***
Dalc         -0.5245     0.1618  -3.242  0.00125 ** 
Walc         -0.1060     0.1184  -0.895  0.37114    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.996 on 643 degrees of freedom
Multiple R-squared:  0.1467,    Adjusted R-squared:  0.1401 
F-statistic: 22.11 on 5 and 643 DF,  p-value: < 2.2e-16

coefplot(modelPor_Multi, title ='Coefficient Plot for modelPor_Multi model')

modelMath_Multi <- lm(G3 ~ Medu + Fedu + studytime + Dalc + Walc , data = mathData)
summary(modelMath_Multi)

Call:
lm(formula = G3 ~ Medu + Fedu + studytime + Dalc + Walc, data = mathData)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.4099  -1.8812   0.4922   3.0686   8.7659 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  7.27335    1.02407   7.102 5.87e-12 ***
Medu         0.80668    0.26555   3.038  0.00254 ** 
Fedu         0.13993    0.26589   0.526  0.59901    
studytime    0.42755    0.27917   1.532  0.12645    
Dalc        -0.25334    0.33370  -0.759  0.44820    
Walc         0.03321    0.23389   0.142  0.88717    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.478 on 389 degrees of freedom
Multiple R-squared:  0.05679,   Adjusted R-squared:  0.04467 
F-statistic: 4.684 on 5 and 389 DF,  p-value: 0.0003635

coefplot(modelMath_Multi,title ='Coefficient Plot for modelMath_Multi model')

####Let’s do Correlation Matrix #### Correlation is not causation!!!!

corMath <- cor(mathData)
corrplot(corMath)

corPor <- cor(porData)
corrplot(corPor)

Let’s focus only on G3

G3Por_cor <- corPor[,'G3']
plot_ly(x = names(G3Por_cor), y = G3Por_cor, type = 'bar') %>%
  layout(title = "Correlation of Final Grade(G3) with Other Variables for Portuguese Data", yaxis = list(title = "Correlation Coefficient"))

G3Math_cor <- corMath[,'G3']
plot_ly(x = names(G3Math_cor), y = G3Math_cor, type = 'bar') %>%
  layout(title = "Correlation of Final Grade(G3) with Other Variables for Math Data", yaxis = list(title = "Correlation Coefficient"))

sorted_names <- names(sort(G3Por_cor))
factor_names <- factor(names(G3Por_cor), levels = sorted_names)


plot_ly(x = factor_names, y = G3Por_cor, type = 'bar') %>%
  layout(title = "Correlation of G3 with Other Variables in Increasing Order for Portuguese Data", 
         yaxis = list(title = "Correlation Coefficient"))

# For Math Data
sorted_names <- names(sort(G3Math_cor))
factor_names <- factor(names(G3Math_cor), levels = sorted_names)


plot_ly(x = factor_names, y = G3Math_cor, type = 'bar') %>%
  layout(title = "Correlation of G3 with Other Variables in Increasing Order for Math Data", 
         yaxis = list(title = "Correlation Coefficient"))

Dropping G1,G2

mathData <- mathData %>% select(-G1, -G2)
porData <- porData %>% select(-G1, -G2)

G3Por_cor <-  cor(porData)[,'G3']
G3Math_cor <-  cor(mathData)[,'G3']
  
sorted_names <- names(sort(G3Por_cor))
factor_names <- factor(names(G3Por_cor), levels = sorted_names)


plot_ly(x = factor_names, y = G3Por_cor, type = 'bar') %>%
  layout(title = "Correlation of G3 with Other Variables in Increasing Order for Portuguese Data", 
         yaxis = list(title = "Correlation Coefficient"))

# For Math Data
sorted_names <- names(sort(G3Math_cor))
factor_names <- factor(names(G3Math_cor), levels = sorted_names)


plot_ly(x = factor_names, y = G3Math_cor, type = 'bar') %>%
  layout(title = "Correlation of G3 with Other Variables in Increasing Order for Math Data", 
         yaxis = list(title = "Correlation Coefficient"))

NA
NA

Let’s Include all of the features and build a linear regression model for 2 datasets:

set.seed(123)
cat('\n\n--------------For Portuguese Data--------------\n\n')

--------------For Portuguese Data--------------

split = sample.split(porData$G3, SplitRatio = 0.8)
train_data = subset(porData, split == TRUE)
test_data = subset(porData, split == FALSE)


model <- lm(G3 ~ ., data = train_data)  
print(summary(model))

Call:
lm(formula = G3 ~ ., data = train_data)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.8424  -1.4794   0.0023   1.4845   7.4442 

Coefficients: (4 not defined because of singularities)
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)      10.595056   2.426206   4.367 1.54e-05 ***
school           -1.002573   0.298814  -3.355 0.000856 ***
sex              -0.570677   0.281030  -2.031 0.042840 *  
age               0.123936   0.112631   1.100 0.271721    
address          -0.366429   0.295274  -1.241 0.215219    
famsize           0.366823   0.272491   1.346 0.178878    
Pstatus           0.172506   0.388575   0.444 0.657282    
Medu              0.030633   0.169053   0.181 0.856285    
Fedu              0.151645   0.154765   0.980 0.327657    
traveltime        0.083146   0.178179   0.467 0.640968    
studytime         0.342011   0.157634   2.170 0.030523 *  
failures         -1.583033   0.227284  -6.965 1.09e-11 ***
schoolsup        -1.140145   0.408453  -2.791 0.005458 ** 
famsup            0.130538   0.252790   0.516 0.605820    
paid             -0.433639   0.593443  -0.731 0.465309    
activities        0.499374   0.251682   1.984 0.047809 *  
nursery          -0.321192   0.310804  -1.033 0.301927    
higher            2.087402   0.436772   4.779 2.34e-06 ***
internet          0.145208   0.305052   0.476 0.634284    
romantic         -0.459084   0.258972  -1.773 0.076910 .  
famrel            0.144389   0.129589   1.114 0.265750    
freetime         -0.109753   0.125437  -0.875 0.382031    
goout             0.040540   0.127380   0.318 0.750426    
Dalc             -0.276450   0.174284  -1.586 0.113353    
Walc             -0.067564   0.135947  -0.497 0.619425    
health           -0.150171   0.086810  -1.730 0.084295 .  
absences         -0.028027   0.027945  -1.003 0.316396    
Mjobat_home      -0.616686   0.557737  -1.106 0.269413    
Mjobhealth        0.301072   0.599020   0.503 0.615471    
Mjobother        -0.574547   0.492701  -1.166 0.244146    
Mjobservices     -0.398453   0.481010  -0.828 0.407874    
Mjobteacher             NA         NA      NA       NA    
Fjobat_home      -0.631090   0.737575  -0.856 0.392630    
Fjobhealth       -1.367956   0.836118  -1.636 0.102478    
Fjobother        -0.556288   0.588647  -0.945 0.345120    
Fjobservices     -0.911826   0.601177  -1.517 0.129992    
Fjobteacher             NA         NA      NA       NA    
reasoncourse     -0.273371   0.338073  -0.809 0.419138    
reasonhome       -0.008687   0.370506  -0.023 0.981303    
reasonother      -0.543228   0.468622  -1.159 0.246950    
reasonreputation        NA         NA      NA       NA    
guardianfather   -0.612864   0.621041  -0.987 0.324221    
guardianmother   -0.908096   0.572423  -1.586 0.113305    
guardianother           NA         NA      NA       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.671 on 480 degrees of freedom
Multiple R-squared:  0.3713,    Adjusted R-squared:  0.3202 
F-statistic: 7.268 on 39 and 480 DF,  p-value: < 2.2e-16

# for Math Data
cat('\n\n--------------For Math Data--------------\n\n')

--------------For Math Data--------------

split = sample.split(mathData$G3, SplitRatio = 0.8)
train_data = subset(mathData, split == TRUE)
test_data = subset(mathData, split == FALSE)


modelMath <- lm(G3 ~ ., data = train_data)  
print(summary(modelMath))

Call:
lm(formula = G3 ~ ., data = train_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-13.760  -2.062   0.311   2.613   7.814 

Coefficients: (4 not defined because of singularities)
                 Estimate Std. Error t value Pr(>|t|)    
(Intercept)      20.41831    5.60320   3.644  0.00032 ***
school            1.39175    0.85952   1.619  0.10654    
sex               1.08939    0.54982   1.981  0.04854 *  
age              -0.41581    0.24952  -1.666  0.09675 .  
address          -0.49086    0.63513  -0.773  0.44027    
famsize           0.47400    0.53699   0.883  0.37816    
Pstatus          -0.34959    0.83489  -0.419  0.67574    
Medu              0.38375    0.35351   1.086  0.27862    
Fedu             -0.09021    0.30754  -0.293  0.76949    
traveltime       -0.42055    0.38289  -1.098  0.27300    
studytime         0.75869    0.31843   2.383  0.01786 *  
failures         -1.82335    0.39302  -4.639 5.39e-06 ***
schoolsup        -1.70011    0.75385  -2.255  0.02490 *  
famsup           -1.31462    0.52507  -2.504  0.01286 *  
paid              0.15593    0.52576   0.297  0.76701    
activities       -0.47595    0.49367  -0.964  0.33582    
nursery          -0.13653    0.62434  -0.219  0.82706    
higher           -0.81942    1.28562  -0.637  0.52441    
internet          0.65831    0.67124   0.981  0.32758    
romantic         -1.09035    0.51121  -2.133  0.03381 *  
famrel            0.20636    0.27044   0.763  0.44607    
freetime          0.41741    0.26704   1.563  0.11917    
goout            -0.80849    0.24645  -3.281  0.00117 ** 
Dalc             -0.24910    0.37181  -0.670  0.50343    
Walc              0.36805    0.28345   1.298  0.19519    
health           -0.14291    0.18535  -0.771  0.44135    
absences          0.08098    0.03510   2.307  0.02178 *  
Mjobat_home       0.52898    1.13016   0.468  0.64011    
Mjobhealth        2.38136    1.00162   2.378  0.01811 *  
Mjobother         0.84924    0.91205   0.931  0.35259    
Mjobservices      1.96054    0.85268   2.299  0.02223 *  
Mjobteacher            NA         NA      NA       NA    
Fjobat_home      -1.80303    1.45869  -1.236  0.21748    
Fjobhealth       -1.87288    1.49097  -1.256  0.21012    
Fjobother        -3.02958    1.04472  -2.900  0.00403 ** 
Fjobservices     -2.74051    1.07082  -2.559  0.01102 *  
Fjobteacher            NA         NA      NA       NA    
reasoncourse     -0.63484    0.64778  -0.980  0.32793    
reasonhome       -0.42988    0.66502  -0.646  0.51854    
reasonother       0.26341    0.92462   0.285  0.77594    
reasonreputation       NA         NA      NA       NA    
guardianfather   -1.10625    1.13885  -0.971  0.33220    
guardianmother   -1.06594    1.04171  -1.023  0.30708    
guardianother          NA         NA      NA       NA    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.064 on 278 degrees of freedom
Multiple R-squared:  0.3091,    Adjusted R-squared:  0.2122 
F-statistic: 3.189 on 39 and 278 DF,  p-value: 1.363e-08

Dropping additional Features

porData <- porData %>% select(-Mjobteacher, -Fjobteacher,-reasonreputation,-guardianother)
mathData <- mathData %>% select(-Mjobteacher, -Fjobteacher,-reasonreputation,-guardianother)

set.seed(123)

# For Portuguese Data
cat('\n\n--------------For Portuguese Data--------------\n\n')

--------------For Portuguese Data--------------

split = sample.split(porData$G3, SplitRatio = 0.8)
train_data = subset(porData, split == TRUE)
test_data = subset(porData, split == FALSE)

model <- lm(G3 ~ ., data = train_data)  
print(summary(model))

Call:
lm(formula = G3 ~ ., data = train_data)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.8424  -1.4794   0.0023   1.4845   7.4442 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    10.595056   2.426206   4.367 1.54e-05 ***
school         -1.002573   0.298814  -3.355 0.000856 ***
sex            -0.570677   0.281030  -2.031 0.042840 *  
age             0.123936   0.112631   1.100 0.271721    
address        -0.366429   0.295274  -1.241 0.215219    
famsize         0.366823   0.272491   1.346 0.178878    
Pstatus         0.172506   0.388575   0.444 0.657282    
Medu            0.030633   0.169053   0.181 0.856285    
Fedu            0.151645   0.154765   0.980 0.327657    
traveltime      0.083146   0.178179   0.467 0.640968    
studytime       0.342011   0.157634   2.170 0.030523 *  
failures       -1.583033   0.227284  -6.965 1.09e-11 ***
schoolsup      -1.140145   0.408453  -2.791 0.005458 ** 
famsup          0.130538   0.252790   0.516 0.605820    
paid           -0.433639   0.593443  -0.731 0.465309    
activities      0.499374   0.251682   1.984 0.047809 *  
nursery        -0.321192   0.310804  -1.033 0.301927    
higher          2.087402   0.436772   4.779 2.34e-06 ***
internet        0.145208   0.305052   0.476 0.634284    
romantic       -0.459084   0.258972  -1.773 0.076910 .  
famrel          0.144389   0.129589   1.114 0.265750    
freetime       -0.109753   0.125437  -0.875 0.382031    
goout           0.040540   0.127380   0.318 0.750426    
Dalc           -0.276450   0.174284  -1.586 0.113353    
Walc           -0.067564   0.135947  -0.497 0.619425    
health         -0.150171   0.086810  -1.730 0.084295 .  
absences       -0.028027   0.027945  -1.003 0.316396    
Mjobat_home    -0.616686   0.557737  -1.106 0.269413    
Mjobhealth      0.301072   0.599020   0.503 0.615471    
Mjobother      -0.574547   0.492701  -1.166 0.244146    
Mjobservices   -0.398453   0.481010  -0.828 0.407874    
Fjobat_home    -0.631090   0.737575  -0.856 0.392630    
Fjobhealth     -1.367956   0.836118  -1.636 0.102478    
Fjobother      -0.556288   0.588647  -0.945 0.345120    
Fjobservices   -0.911826   0.601177  -1.517 0.129992    
reasoncourse   -0.273371   0.338073  -0.809 0.419138    
reasonhome     -0.008687   0.370506  -0.023 0.981303    
reasonother    -0.543228   0.468622  -1.159 0.246950    
guardianfather -0.612864   0.621041  -0.987 0.324221    
guardianmother -0.908096   0.572423  -1.586 0.113305    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.671 on 480 degrees of freedom
Multiple R-squared:  0.3713,    Adjusted R-squared:  0.3202 
F-statistic: 7.268 on 39 and 480 DF,  p-value: < 2.2e-16

# Compute RMSE for Portuguese Data
predicted_values <- predict(model, newdata = test_data)
actual_values <- test_data$G3
rmse_por <- rmse(actual_values, predicted_values)
cat('RMSE for Portuguese Data:', rmse_por, '\n')

RMSE for Portuguese Data: 2.749893 

# For Math Data
cat('\n\n--------------For Math Data--------------\n\n')

--------------For Math Data--------------

split = sample.split(mathData$G3, SplitRatio = 0.8)
train_data = subset(mathData, split == TRUE)
test_data = subset(mathData, split == FALSE)

modelMath <- lm(G3 ~ ., data = train_data)  
print(summary(modelMath))

Call:
lm(formula = G3 ~ ., data = train_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-13.760  -2.062   0.311   2.613   7.814 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)    20.41831    5.60320   3.644  0.00032 ***
school          1.39175    0.85952   1.619  0.10654    
sex             1.08939    0.54982   1.981  0.04854 *  
age            -0.41581    0.24952  -1.666  0.09675 .  
address        -0.49086    0.63513  -0.773  0.44027    
famsize         0.47400    0.53699   0.883  0.37816    
Pstatus        -0.34959    0.83489  -0.419  0.67574    
Medu            0.38375    0.35351   1.086  0.27862    
Fedu           -0.09021    0.30754  -0.293  0.76949    
traveltime     -0.42055    0.38289  -1.098  0.27300    
studytime       0.75869    0.31843   2.383  0.01786 *  
failures       -1.82335    0.39302  -4.639 5.39e-06 ***
schoolsup      -1.70011    0.75385  -2.255  0.02490 *  
famsup         -1.31462    0.52507  -2.504  0.01286 *  
paid            0.15593    0.52576   0.297  0.76701    
activities     -0.47595    0.49367  -0.964  0.33582    
nursery        -0.13653    0.62434  -0.219  0.82706    
higher         -0.81942    1.28562  -0.637  0.52441    
internet        0.65831    0.67124   0.981  0.32758    
romantic       -1.09035    0.51121  -2.133  0.03381 *  
famrel          0.20636    0.27044   0.763  0.44607    
freetime        0.41741    0.26704   1.563  0.11917    
goout          -0.80849    0.24645  -3.281  0.00117 ** 
Dalc           -0.24910    0.37181  -0.670  0.50343    
Walc            0.36805    0.28345   1.298  0.19519    
health         -0.14291    0.18535  -0.771  0.44135    
absences        0.08098    0.03510   2.307  0.02178 *  
Mjobat_home     0.52898    1.13016   0.468  0.64011    
Mjobhealth      2.38136    1.00162   2.378  0.01811 *  
Mjobother       0.84924    0.91205   0.931  0.35259    
Mjobservices    1.96054    0.85268   2.299  0.02223 *  
Fjobat_home    -1.80303    1.45869  -1.236  0.21748    
Fjobhealth     -1.87288    1.49097  -1.256  0.21012    
Fjobother      -3.02958    1.04472  -2.900  0.00403 ** 
Fjobservices   -2.74051    1.07082  -2.559  0.01102 *  
reasoncourse   -0.63484    0.64778  -0.980  0.32793    
reasonhome     -0.42988    0.66502  -0.646  0.51854    
reasonother     0.26341    0.92462   0.285  0.77594    
guardianfather -1.10625    1.13885  -0.971  0.33220    
guardianmother -1.06594    1.04171  -1.023  0.30708    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.064 on 278 degrees of freedom
Multiple R-squared:  0.3091,    Adjusted R-squared:  0.2122 
F-statistic: 3.189 on 39 and 278 DF,  p-value: 1.363e-08

# Compute RMSE for Math Data
predicted_values_math <- predict(modelMath, newdata = test_data)
actual_values_math <- test_data$G3
rmse_math <- rmse(actual_values_math, predicted_values_math)
cat('RMSE for Math Data:', rmse_math, '\n')

RMSE for Math Data: 4.610122 

coefplot(model, title = 'Coefficient Plot for Portuguese Data')

coefplot(modelMath, title = 'Coefficient Plot for Math Data')

Ordered Coeff

coefficients <- coef(model)
sorted_coefficients <- coefficients[order(abs(coefficients), decreasing = TRUE)]
coefplot(model,title='Coefficient Plot for Portuguese Data',  sort = "magnitude")

coefficientsMath <- coef(modelMath)
sorted_coefficientsMath <- coefficientsMath[order(abs(coefficientsMath), decreasing = TRUE)]
coefplot(modelMath,title='Coefficient Plot for Math Data',  sort = "magnitude")

sorted_names <- names(sort(sorted_coefficients))
factor_names <- factor(names(sorted_coefficients), levels = sorted_names)
plot_ly(x = factor_names, y = sorted_coefficients, type = 'bar') %>%
  layout(title = "Sorted Coefficients in Increasing Order for Portuguese Data", 
         yaxis = list(title = "Coefficient Value"))

# For math Data
sorted_names <- names(sort(sorted_coefficientsMath))
factor_names <- factor(names(sorted_coefficientsMath), levels = sorted_names)
plot_ly(x = factor_names, y = sorted_coefficientsMath, type = 'bar') %>%
  layout(title = "Sorted Coefficients in Increasing Order for Math Data", 
         yaxis = list(title = "Coefficient Value"))

NA

important_features_Por <- c("school", "failures", "schoolsup", "higher", "sex", "studytime", "activities", "romantic", "health")

important_features_Math <- c("sex", "studytime", "failures", "schoolsup", "famsup", "romantic", "goout", "absences", "Mjobhealth", "Mjobservices", "Fjobother", "Fjobservices")

set.seed(123)
# Modeling for Portuguese Data
formulaPor <- as.formula(paste("G3 ~", paste(important_features_Por, collapse=" + ")))
model <- lm(formulaPor, data=porData)
summary(model)

Call:
lm(formula = formulaPor, data = porData)

Residuals:
     Min       1Q   Median       3Q      Max 
-11.7674  -1.4722  -0.0888   1.6632   7.7743 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 11.19384    0.53940  20.752  < 2e-16 ***
school      -1.57430    0.23143  -6.802 2.37e-11 ***
failures    -1.49067    0.19056  -7.823 2.15e-14 ***
schoolsup   -1.45680    0.35555  -4.097 4.72e-05 ***
higher       1.99586    0.37067   5.384 1.02e-07 ***
sex         -0.70079    0.22943  -3.054 0.002348 ** 
studytime    0.49433    0.13561   3.645 0.000289 ***
activities   0.23278    0.21659   1.075 0.282882    
romantic    -0.45693    0.22528  -2.028 0.042948 *  
health      -0.18431    0.07447  -2.475 0.013586 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.706 on 639 degrees of freedom
Multiple R-squared:  0.3082,    Adjusted R-squared:  0.2984 
F-statistic: 31.63 on 9 and 639 DF,  p-value: < 2.2e-16

coefficients <- coef(model)
sorted_coefficients <- coefficients[order(abs(coefficients), decreasing = TRUE)]
coefplot(model, title='Coefficient Plot for Portuguese Data',  sort = "magnitude")

predicted_values <- predict(model, newdata = test_data)
actual_values <- test_data$G3
rmse_por <- rmse(actual_values, predicted_values)
cat('RMSE for Portuguese Data:', rmse_por, '\n')

RMSE for Portuguese Data: 4.260732 

# Modeling for Math Data
formulaMath <- as.formula(paste("G3 ~", paste(important_features_Math, collapse=" + ")))
modelMath <- lm(formulaMath, data=mathData)
summary(modelMath)

Call:
lm(formula = formulaMath, data = mathData)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.7405  -1.8524   0.3052   2.6915   8.5256 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  11.77060    1.06696  11.032  < 2e-16 ***
sex           1.25145    0.44404   2.818  0.00508 ** 
studytime     0.53875    0.26488   2.034  0.04265 *  
failures     -2.09888    0.28806  -7.286 1.84e-12 ***
schoolsup    -1.12573    0.63121  -1.783  0.07531 .  
famsup       -0.71675    0.43799  -1.636  0.10256    
romantic     -1.10400    0.45072  -2.449  0.01476 *  
goout        -0.44629    0.18822  -2.371  0.01823 *  
absences      0.05947    0.02636   2.256  0.02463 *  
Mjobhealth    2.37999    0.75824   3.139  0.00183 ** 
Mjobservices  1.47722    0.49133   3.007  0.00282 ** 
Fjobother    -1.12730    0.58200  -1.937  0.05349 .  
Fjobservices -1.11196    0.64556  -1.722  0.08579 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.095 on 382 degrees of freedom
Multiple R-squared:  0.2255,    Adjusted R-squared:  0.2012 
F-statistic: 9.269 on 12 and 382 DF,  p-value: 9.263e-16

coefficientsMath <- coef(modelMath)
sorted_coefficientsMath <- coefficientsMath[order(abs(coefficientsMath), decreasing = TRUE)]
coefplot(modelMath, title='Coefficient Plot for Math Data',  sort = "magnitude")

predicted_values_math <- predict(modelMath, newdata = test_data)
actual_values_math <- test_data$G3
rmse_math <- rmse(actual_values_math, predicted_values_math)
cat('RMSE for Math Data:', rmse_math, '\n')

RMSE for Math Data: 4.170892 

Does alcohol consumption have a significant effect on student performance ?

Adding a new column called ‘Avg_alc’ which is the Average between Weekday Alcohol consumption & Weekend Alcohol consumption.

mathData$Avg_alc <- (mathData$Dalc + mathData$Walc)/2
mathData <- mathData %>% select(-Dalc, -Walc)

porData$Avg_alc <- (porData$Dalc + porData$Walc)/2
porData <- porData %>% select(-Dalc, -Walc)

G3Por_cor <-  cor(porData)[,'G3']
G3Math_cor <-  cor(mathData)[,'G3']
  
sorted_names <- names(sort(G3Por_cor))
factor_names <- factor(names(G3Por_cor), levels = sorted_names)


plot_ly(x = factor_names, y = G3Por_cor, type = 'bar') %>%
  layout(title = "Correlation of G3 with Other Variables in Increasing Order for Portuguese Data", 
         yaxis = list(title = "Correlation Coefficient"))

# For Math Data
sorted_names <- names(sort(G3Math_cor))
factor_names <- factor(names(G3Math_cor), levels = sorted_names)


plot_ly(x = factor_names, y = G3Math_cor, type = 'bar') %>%
  layout(title = "Correlation of G3 with Other Variables in Increasing Order for Math Data", 
         yaxis = list(title = "Correlation Coefficient"))

NA

set.seed(123)

# For Portuguese Data
cat('\n\n--------------For Portuguese Data--------------\n\n')

--------------For Portuguese Data--------------

split = sample.split(porData$G3, SplitRatio = 0.8)
train_data = subset(porData, split == TRUE)
test_data = subset(porData, split == FALSE)

model <- lm(G3 ~ ., data = train_data)  
print(summary(model))

Call:
lm(formula = G3 ~ ., data = train_data)

Residuals:
     Min       1Q   Median       3Q      Max 
-12.8649  -1.4690  -0.0324   1.4546   7.4947 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)    10.65632    2.42383   4.396 1.36e-05 ***
school         -1.01607    0.29816  -3.408  0.00071 ***
sex            -0.56464    0.28080  -2.011  0.04490 *  
age             0.11966    0.11244   1.064  0.28779    
address        -0.36487    0.29514  -1.236  0.21696    
famsize         0.37507    0.27216   1.378  0.16880    
Pstatus         0.17681    0.38837   0.455  0.64913    
Medu            0.01999    0.16840   0.119  0.90557    
Fedu            0.15936    0.15437   1.032  0.30242    
traveltime      0.07806    0.17798   0.439  0.66114    
studytime       0.33635    0.15739   2.137  0.03310 *  
failures       -1.57897    0.22712  -6.952 1.18e-11 ***
schoolsup      -1.16414    0.40707  -2.860  0.00442 ** 
famsup          0.11970    0.25228   0.474  0.63537    
paid           -0.45206    0.59270  -0.763  0.44600    
activities      0.49781    0.25156   1.979  0.04840 *  
nursery        -0.31702    0.31062  -1.021  0.30796    
higher          2.08859    0.43658   4.784 2.29e-06 ***
internet        0.14621    0.30492   0.480  0.63179    
romantic       -0.46852    0.25856  -1.812  0.07061 .  
famrel          0.14097    0.12946   1.089  0.27673    
freetime       -0.11918    0.12477  -0.955  0.33997    
goout           0.05859    0.12511   0.468  0.63980    
health         -0.14354    0.08634  -1.663  0.09705 .  
absences       -0.02791    0.02793  -0.999  0.31823    
Mjobat_home    -0.62030    0.55748  -1.113  0.26639    
Mjobhealth      0.34049    0.59653   0.571  0.56842    
Mjobother      -0.58721    0.49221  -1.193  0.23346    
Mjobservices   -0.40723    0.48066  -0.847  0.39729    
Fjobat_home    -0.61661    0.73701  -0.837  0.40321    
Fjobhealth     -1.37558    0.83570  -1.646  0.10041    
Fjobother      -0.53498    0.58773  -0.910  0.36315    
Fjobservices   -0.89124    0.60031  -1.485  0.13830    
reasoncourse   -0.28587    0.33753  -0.847  0.39745    
reasonhome     -0.03253    0.36903  -0.088  0.92979    
reasonother    -0.58365    0.46542  -1.254  0.21044    
guardianfather -0.60289    0.62063  -0.971  0.33183    
guardianmother -0.87823    0.57084  -1.538  0.12458    
Avg_alc        -0.31080    0.14491  -2.145  0.03247 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.67 on 481 degrees of freedom
Multiple R-squared:  0.3705,    Adjusted R-squared:  0.3208 
F-statistic:  7.45 on 38 and 481 DF,  p-value: < 2.2e-16

# Compute RMSE for Portuguese Data
predicted_values <- predict(model, newdata = test_data)
actual_values <- test_data$G3
rmse_por <- rmse(actual_values, predicted_values)
cat('RMSE for Portuguese Data:', rmse_por, '\n')

RMSE for Portuguese Data: 2.74529 

# For Math Data
cat('\n\n--------------For Math Data--------------\n\n')

--------------For Math Data--------------

split = sample.split(mathData$G3, SplitRatio = 0.8)
train_data = subset(mathData, split == TRUE)
test_data = subset(mathData, split == FALSE)

modelMath <- lm(G3 ~ ., data = train_data)  
print(summary(modelMath))

Call:
lm(formula = G3 ~ ., data = train_data)

Residuals:
    Min      1Q  Median      3Q     Max 
-13.796  -1.941   0.337   2.661   7.693 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)    21.00200    5.57812   3.765 0.000203 ***
school          1.35881    0.85920   1.581 0.114900    
sex             1.10007    0.54988   2.001 0.046408 *  
age            -0.43299    0.24907  -1.738 0.083235 .  
address        -0.48185    0.63524  -0.759 0.448771    
famsize         0.46514    0.53706   0.866 0.387187    
Pstatus        -0.30511    0.83407  -0.366 0.714791    
Medu            0.32002    0.34856   0.918 0.359346    
Fedu           -0.04950    0.30526  -0.162 0.871291    
traveltime     -0.45310    0.38178  -1.187 0.236318    
studytime       0.74948    0.31840   2.354 0.019272 *  
failures       -1.85267    0.39217  -4.724 3.67e-06 ***
schoolsup      -1.70497    0.75404  -2.261 0.024522 *  
famsup         -1.35127    0.52409  -2.578 0.010441 *  
paid            0.16646    0.52581   0.317 0.751796    
activities     -0.46764    0.49374  -0.947 0.344385    
nursery        -0.13691    0.62450  -0.219 0.826625    
higher         -0.96184    1.27907  -0.752 0.452695    
internet        0.64538    0.67131   0.961 0.337197    
romantic       -1.07531    0.51116  -2.104 0.036301 *  
famrel          0.19819    0.27040   0.733 0.464198    
freetime        0.38454    0.26534   1.449 0.148395    
goout          -0.75222    0.24085  -3.123 0.001977 ** 
health         -0.14243    0.18540  -0.768 0.442999    
absences        0.08333    0.03504   2.378 0.018073 *  
Mjobat_home     0.42393    1.12619   0.376 0.706888    
Mjobhealth      2.43241    1.00075   2.431 0.015705 *  
Mjobother       0.70353    0.90209   0.780 0.436116    
Mjobservices    1.87902    0.84950   2.212 0.027783 *  
Fjobat_home    -1.86253    1.45802  -1.277 0.202510    
Fjobhealth     -1.92779    1.49048  -1.293 0.196943    
Fjobother      -2.92886    1.04075  -2.814 0.005238 ** 
Fjobservices   -2.70820    1.07068  -2.529 0.011976 *  
reasoncourse   -0.67507    0.64686  -1.044 0.297570    
reasonhome     -0.46557    0.66436  -0.701 0.484019    
reasonother     0.10717    0.91329   0.117 0.906672    
guardianfather -1.07906    1.13886  -0.947 0.344212    
guardianmother -1.03534    1.04159  -0.994 0.321085    
Avg_alc         0.22662    0.30861   0.734 0.463367    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.065 on 279 degrees of freedom
Multiple R-squared:  0.3063,    Adjusted R-squared:  0.2118 
F-statistic: 3.241 on 38 and 279 DF,  p-value: 1.114e-08

# Compute RMSE for Math Data
predicted_values_math <- predict(modelMath, newdata = test_data)
actual_values_math <- test_data$G3
rmse_math <- rmse(actual_values_math, predicted_values_math)
cat('RMSE for Math Data:', rmse_math, '\n')

RMSE for Math Data: 4.619303 

coefficients <- coef(model)
sorted_coefficients <- coefficients[order(abs(coefficients), decreasing = TRUE)]
sorted_names <- names(sort(sorted_coefficients))
factor_names <- factor(names(sorted_coefficients), levels = sorted_names)
plot_ly(x = factor_names, y = sorted_coefficients, type = 'bar') %>%
  layout(title = "Sorted Coefficients in Increasing Order for Portuguese Data", 
         yaxis = list(title = "Coefficient Value"))

# For math Data
coefficientsMath <- coef(modelMath)
sorted_coefficientsMath <- coefficientsMath[order(abs(coefficientsMath), decreasing = TRUE)]
sorted_names <- names(sort(sorted_coefficientsMath))
factor_names <- factor(names(sorted_coefficientsMath), levels = sorted_names)
plot_ly(x = factor_names, y = sorted_coefficientsMath, type = 'bar') %>%
  layout(title = "Sorted Coefficients in Increasing Order for Math Data", 
         yaxis = list(title = "Coefficient Value"))

NA

combinedData <- rbind(mathData, porData)

View(combinedData)

corValues <- cor(combinedData)
AlcAll_cor <-  cor(combinedData)[,'Avg_alc']
  
sorted_names <- names(sort(AlcAll_cor))
factor_names <- factor(names(AlcAll_cor), levels = sorted_names)


plot_ly(x = factor_names, y = AlcAll_cor, type = 'bar') %>%
  layout(title = "Correlation of Avg_alc with Other Variables in Increasing Order for Combined data", 
         yaxis = list(title = "Correlation Coefficient"))

cat('\n\n--------------For Combined Data--------------\n\n')

--------------For Combined Data--------------

split = sample.split(combinedData$Avg_alc, SplitRatio = 0.8)
train_data = subset(combinedData, split == TRUE)
test_data = subset(combinedData, split == FALSE)

modelAll <- lm(Avg_alc ~ ., data = train_data)  
print(summary(modelAll))

Call:
lm(formula = Avg_alc ~ ., data = train_data)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.87298 -0.55788 -0.09884  0.42136  3.08504 

Coefficients:
                Estimate Std. Error t value Pr(>|t|)    
(Intercept)    -0.212289   0.618233  -0.343 0.731403    
school          0.019069   0.076548   0.249 0.803340    
sex             0.575101   0.063773   9.018  < 2e-16 ***
age             0.067855   0.027271   2.488 0.013044 *  
address         0.128984   0.071675   1.800 0.072310 .  
famsize         0.136354   0.064166   2.125 0.033891 *  
Pstatus         0.046166   0.097483   0.474 0.635930    
Medu            0.017123   0.040828   0.419 0.675043    
Fedu            0.025090   0.036432   0.689 0.491227    
traveltime      0.055761   0.043399   1.285 0.199216    
studytime      -0.140734   0.036894  -3.815 0.000147 ***
failures        0.005874   0.050611   0.116 0.907632    
schoolsup       0.120645   0.096340   1.252 0.210836    
famsup          0.033660   0.061422   0.548 0.583833    
paid            0.147789   0.072547   2.037 0.041966 *  
activities     -0.088996   0.058999  -1.508 0.131836    
nursery        -0.172589   0.071919  -2.400 0.016634 *  
higher         -0.071643   0.118568  -0.604 0.545859    
internet        0.030993   0.075741   0.409 0.682501    
romantic        0.072490   0.061485   1.179 0.238750    
famrel         -0.209515   0.031013  -6.756 2.74e-11 ***
freetime        0.011326   0.030188   0.375 0.707632    
goout           0.318226   0.026359  12.073  < 2e-16 ***
health          0.059558   0.021262   2.801 0.005216 ** 
absences        0.017552   0.004816   3.645 0.000285 ***
G3             -0.002976   0.008139  -0.366 0.714719    
Mjobat_home     0.026614   0.133563   0.199 0.842109    
Mjobhealth     -0.283918   0.134431  -2.112 0.034997 *  
Mjobother      -0.149291   0.112653  -1.325 0.185474    
Mjobservices   -0.101318   0.107234  -0.945 0.345032    
Fjobat_home     0.135014   0.179394   0.753 0.451907    
Fjobhealth      0.282642   0.188363   1.501 0.133875    
Fjobother       0.332376   0.133422   2.491 0.012935 *  
Fjobservices    0.529629   0.136397   3.883 0.000112 ***
reasoncourse   -0.076977   0.078567  -0.980 0.327497    
reasonhome     -0.026409   0.084473  -0.313 0.754645    
reasonother     0.214595   0.113489   1.891 0.059003 .  
guardianfather  0.223536   0.143051   1.563 0.118536    
guardianmother  0.073268   0.132245   0.554 0.579716    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8025 on 796 degrees of freedom
Multiple R-squared:  0.3773,    Adjusted R-squared:  0.3476 
F-statistic: 12.69 on 38 and 796 DF,  p-value: < 2.2e-16

predicted_values_math <- predict(modelAll, newdata = test_data)
actual_values_math <- test_data$Avg_alc
rmse_math <- rmse(actual_values_math, predicted_values_math)
cat('RMSE for All Data for Alcohol Consumption:', rmse_math, '\n')

RMSE for All Data for Alcohol Consumption: 0.8816963 

coefficients <- coef(modelAll)
sorted_coefficients <- coefficients[order(abs(coefficients), decreasing = TRUE)]
sorted_names <- names(sort(sorted_coefficients))
factor_names <- factor(names(sorted_coefficients), levels = sorted_names)
plot_ly(x = factor_names, y = sorted_coefficients, type = 'bar') %>%
  layout(title = "Sorted Coefficients in Increasing Order for Alcohol Consumption for combined Data ", 
         yaxis = list(title = "Coefficient Value"))